RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.74 18.1605 0.621218
2 to 25 15.78 16.7227 0.526701
3 to 26 15.88 13.4955 0.297562
4 to 27 15.95 9.5641 0.079112
5 to 28 15.58 26.5226 0.934548
6 to 29 15.85 9.0472 0.061232
7 to 30 15.88 18.7243 0.655418
8 to 31 15.71 15.7177 0.456073
9 to 32 15.70 20.1976 0.735754
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.961757
Tough bday spacings test for dh-ranFile-2018-07-09_06:31: 4096 birthdays, year=2^32 days
Table of Expected vs. Observed counts:
Duplicates 0 1 2 3 4 5 6 7 8 9 >=10
Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1
Observed 13 28 68 120 87 84 49 27 16 7 1
(O-E)^2/E 1.6 2.0 0.4 5.1 1.2 0.4 0.2 0.3 0.1 0.0 2.3
Birthday Spacings: Sum(O-E)^2/E= 13.589, p= 0.807
RESULTS OF GCD FOR dh-ranFile-2018-07-09_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.150609
p-value, dist. of gcd's: 0.579017
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.356 0.712 0.837 0.577 0.290 0.238 0.451 0.510
Bits 8 to 15---> 0.239 0.963 0.973 0.055 0.893 0.846 0.806 0.396
Bits 16 to 23---> 0.846 0.162 0.574 0.312 0.213 0.576 0.714 0.064
Bits 24 to 31---> 0.816 0.099 0.592 0.124 0.576 0.988 0.916 0.559
KS test for the above 32 p values: 0.269
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_06:31,
p-values for 5 runs: 0.2987, 0.4973, 0.8536, 0.7636, 0.8919
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 215 211.4 0.061 0.061
r= 29 5154 5134.0 0.078 0.139
r= 30 23089 23103.0 0.009 0.147
r= 31 11542 11551.5 0.008 0.155
chi-square = 0.155 with df = 3; p-value = 0.015
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 188 211.4 2.594 2.594
r= 30 5093 5134.0 0.328 2.922
r= 31 23035 23103.0 0.200 3.122
r= 32 11684 11551.5 1.519 4.641
chi-square = 4.641 with df = 3; p-value = 0.800
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_06:31
b-rank test for bits 1 to 8, p=0.10819
b-rank test for bits 2 to 9, p=0.27858
b-rank test for bits 3 to 10, p=0.40772
b-rank test for bits 4 to 11, p=0.60865
b-rank test for bits 5 to 12, p=0.58593
b-rank test for bits 6 to 13, p=0.92889
b-rank test for bits 7 to 14, p=0.87164
b-rank test for bits 8 to 15, p=0.04278
b-rank test for bits 9 to 16, p=0.28683
b-rank test for bits 10 to 17, p=0.45792
b-rank test for bits 11 to 18, p=0.51296
b-rank test for bits 12 to 19, p=0.00094
b-rank test for bits 13 to 20, p=0.87638
b-rank test for bits 14 to 21, p=0.07267
b-rank test for bits 15 to 22, p=0.32028
b-rank test for bits 16 to 23, p=0.68828
b-rank test for bits 17 to 24, p=0.43798
b-rank test for bits 18 to 25, p=0.84312
b-rank test for bits 19 to 26, p=0.48120
b-rank test for bits 20 to 27, p=0.58119
b-rank test for bits 21 to 28, p=0.65198
b-rank test for bits 22 to 29, p=0.01742
b-rank test for bits 23 to 30, p=0.36045
b-rank test for bits 24 to 31, p=0.56228
b-rank test for bits 25 to 32, p=0.87205
TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices
The above should be 25 uniform [0,1] random variables:
The KS test for those 25 supposed UNI's yields p = 0.615352
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_06:31
(20 bits/word, 2097152 words 20 bitstreams. No. missing words
should average 141909.33 with sigma=428.00.)
----------------------------------------------------------------
BITSTREAM test results.
Bitstream No. missing words z-score p-value
1 141695 -0.50 0.308266
2 141865 -0.10 0.458753
3 141433 -1.11 0.132871
4 141380 -1.24 0.108090
5 141074 -1.95 0.025487
6 141770 -0.33 0.372387
7 141973 0.15 0.559129
8 142083 0.41 0.657545
9 142106 0.46 0.677066
10 141317 -1.38 0.083187
11 141872 -0.09 0.465249
12 141718 -0.45 0.327426
13 141742 -0.39 0.347914
14 141864 -0.11 0.457826
15 142391 1.13 0.869790
16 142178 0.63 0.734911
17 141425 -1.13 0.128899
18 141728 -0.42 0.335904
19 141549 -0.84 0.199924
20 141985 0.18 0.570167
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_06:31
Bits used No. missing words z-score p-value
23 to 32 141567 -1.1804 0.118911
22 to 31 141752 -0.5425 0.293731
21 to 30 141301 -2.0977 0.017966
20 to 29 141450 -1.5839 0.056609
19 to 28 142130 0.7609 0.776651
18 to 27 141658 -0.8667 0.193066
17 to 26 141968 0.2023 0.580163
16 to 25 141553 -1.2287 0.109588
15 to 24 141863 -0.1598 0.436536
14 to 23 141620 -0.9977 0.159215
13 to 22 142096 0.6437 0.740112
12 to 21 142310 1.3816 0.916456
11 to 20 141815 -0.3253 0.372486
10 to 19 141915 0.0196 0.507800
9 to 18 141340 -1.9632 0.024811
8 to 17 141450 -1.5839 0.056609
7 to 16 141895 -0.0494 0.480295
6 to 15 142055 0.5023 0.692275
5 to 14 141518 -1.3494 0.088602
4 to 13 142095 0.6402 0.738992
3 to 12 141799 -0.3804 0.351806
2 to 11 142018 0.3747 0.646067
1 to 10 141958 0.1678 0.566641
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_06:31
Bits used No. missing words z-score p-value
28 to 32 142623 2.4192 0.992223
27 to 31 141974 0.2192 0.586761
26 to 30 141833 -0.2587 0.397916
25 to 29 141815 -0.3198 0.374574
24 to 28 141728 -0.6147 0.269384
23 to 27 141738 -0.5808 0.280695
22 to 26 141460 -1.5232 0.063860
21 to 25 141878 -0.1062 0.457711
20 to 24 142107 0.6701 0.748593
19 to 23 141738 -0.5808 0.280695
18 to 22 142167 0.8735 0.808793
17 to 21 141657 -0.8554 0.196177
16 to 20 142157 0.8396 0.799422
15 to 19 141905 -0.0147 0.494145
14 to 18 142477 1.9243 0.972842
13 to 17 141659 -0.8486 0.198059
12 to 16 141731 -0.6045 0.272753
11 to 15 142243 1.1311 0.870990
10 to 14 141427 -1.6350 0.051023
9 to 13 142075 0.5616 0.712803
8 to 12 141873 -0.1232 0.450993
7 to 11 142062 0.5175 0.697605
6 to 10 141659 -0.8486 0.198059
5 to 9 141979 0.2362 0.593349
4 to 8 141882 -0.0926 0.463093
3 to 7 141902 -0.0248 0.490088
2 to 6 141820 -0.3028 0.381016
1 to 5 142151 0.8192 0.793670
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_06:31
Bits used No. missing words z-score p-value
31 to 32 142885 2.8781 0.997999
30 to 31 142361 1.3324 0.908629
29 to 30 141723 -0.5496 0.291281
28 to 29 142162 0.7453 0.771967
27 to 28 141803 -0.3137 0.376891
26 to 27 141795 -0.3373 0.367962
25 to 26 141965 0.1642 0.565220
24 to 25 141999 0.2645 0.604308
23 to 24 142318 1.2055 0.885998
22 to 23 142214 0.8987 0.815602
21 to 22 142276 1.0816 0.860290
20 to 21 142324 1.2232 0.889376
19 to 20 142146 0.6981 0.757456
18 to 19 141628 -0.8299 0.203303
17 to 18 141853 -0.1662 0.434014
16 to 17 141688 -0.6529 0.256913
15 to 16 141899 -0.0305 0.487845
14 to 15 141617 -0.8623 0.194253
13 to 14 141949 0.1170 0.546578
12 to 13 141786 -0.3638 0.358002
11 to 12 141788 -0.3579 0.360207
10 to 11 142435 1.5506 0.939507
9 to 10 142151 0.7129 0.762043
8 to 9 141510 -1.1780 0.119405
7 to 8 141909 -0.0010 0.499612
6 to 7 142573 1.9577 0.974869
5 to 6 141710 -0.5880 0.278268
4 to 5 142070 0.4740 0.682233
3 to 4 142536 1.8486 0.967741
2 to 3 142355 1.3147 0.905688
1 to 2 141688 -0.6529 0.256913
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2484.32 -0.222 0.412258
Test results for specific bytes for dh-ranFile-2018-07-09_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2565.21 0.922 0.821794
2 to 9 2526.47 0.374 0.645918
3 to 10 2546.17 0.653 0.743120
4 to 11 2474.59 -0.359 0.359692
5 to 12 2536.65 0.518 0.697870
6 to 13 2523.56 0.333 0.630491
7 to 14 2409.28 -1.283 0.099750
8 to 15 2482.63 -0.246 0.402960
9 to 16 2591.08 1.288 0.901127
10 to 17 2483.74 -0.230 0.409063
11 to 18 2455.43 -0.630 0.264250
12 to 19 2589.25 1.262 0.896564
13 to 20 2478.60 -0.303 0.381093
14 to 21 2492.90 -0.100 0.460002
15 to 22 2509.96 0.141 0.555988
16 to 23 2440.20 -0.846 0.198863
17 to 24 2565.94 0.932 0.824456
18 to 25 2598.95 1.399 0.919149
19 to 26 2477.89 -0.313 0.377248
20 to 27 2405.08 -1.342 0.089728
21 to 28 2503.43 0.049 0.519348
22 to 29 2499.83 -0.002 0.499033
23 to 30 2490.80 -0.130 0.448266
24 to 31 2496.58 -0.048 0.480733
25 to 32 2483.27 -0.237 0.406465
CDPARK for dh-ranFile-2018-07-09_06:31: result of 10 tests
(Of 12000 tries, the average no. of successes should be
3523.0 with sigma=21.9)
No. succeses z-score p-value
3500 -1.0502 0.146807
3527 0.1826 0.572463
3537 0.6393 0.738676
3533 0.4566 0.676028
3558 1.5982 0.944998
3501 -1.0046 0.157553
3517 -0.2740 0.392053
3489 -1.5525 0.060270
3531 0.3653 0.642555
3522 -0.0457 0.481790
Square side=100, avg. no. parked=3521.50 sample std.=19.45
p-value of the KSTEST for those 10 p-values: 0.971561
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_06:31
0.4640,0.6957,0.9909,0.4774,0.1203,0.8472,0.5112,0.1254,0.8296,0.1960,
The KS test for those 10 p-values: 0.886758
The 3DSPHERES test for dh-ranFile-2018-07-09_06:31
sample no r^3 equiv. uni.
1 62.276 0.874553
2 26.091 0.580926
3 1.568 0.050921
4 0.737 0.024256
5 20.764 0.499495
6 10.165 0.287395
7 43.120 0.762441
8 47.560 0.795123
9 62.725 0.876417
10 27.245 0.596735
11 50.995 0.817284
12 40.198 0.738139
13 12.760 0.346439
14 14.622 0.385788
15 5.053 0.155003
16 18.151 0.453948
17 10.351 0.291795
18 16.841 0.429566
19 29.312 0.623587
20 39.676 0.733542
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.820420
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.7 0.8 0.2 0.2 -1.4
0.7 -0.4 0.5 0.4 0.1 -0.3
0.2 -0.1 -1.4 0.6 1.2 0.6
-0.5 -0.3 -1.5 0.1 0.3 1.8
-2.3 0.5 0.1 0.9 1.0 -2.2
-0.8 1.9 -0.4 -0.3 2.2 1.3
-0.7 0.5 0.1 -0.7 -1.3 -1.0
-1.1
Chi-square with 42 degrees of freedom:43.123490
z-score=0.122583, p-value=0.576978
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_06:31
Test no p-value
1 0.838691
2 0.907783
3 0.877348
4 0.532599
5 0.817099
6 0.879358
7 0.986734
8 0.191751
9 0.938307
10 0.408458
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.007619
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_06:31:
(for k>=2, the prob. of a run of length k is 2*k/(k+1)!)
Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E
2 66666.67 66605 0.06 66632 0.02
3 25000.00 25085 0.29 24894 0.45
4 6666.67 6680 0.03 6784 2.06
5 1388.89 1350 1.09 1418 0.61
6 238.10 241 0.04 248 0.41
7 34.72 31 0.40 21 5.42
8 4.96 7 0.84 2 1.77
p=0.15867 p=0.90334
Number of rngs required: 689232, p-value: 0.831
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_06:31
No. of wins: Observed Expected
98661 98585.9
z-score= 0.336, pvalue=0.63159
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66818 66666.7 0.344 0.344
2 37406 37654.3 1.638 1.981
3 26902 26954.7 0.103 2.084
4 19413 19313.5 0.513 2.597
5 13791 13851.4 0.264 2.861
6 10089 9943.5 2.128 4.989
7 7174 7145.0 0.117 5.106
8 5080 5139.1 0.679 5.785
9 3808 3699.9 3.160 8.946
10 2719 2666.3 1.042 9.987
11 1907 1923.3 0.139 10.126
12 1286 1388.7 7.601 17.727
13 990 1003.7 0.187 17.914
14 685 726.1 2.331 20.245
15 525 525.8 0.001 20.246
16 382 381.2 0.002 20.248
17 253 276.5 2.004 22.252
18 197 200.8 0.073 22.325
19 146 146.0 0.000 22.325
20 120 106.2 1.789 24.114
21 309 287.1 1.668 25.782
Chisq= 25.78 for 20 degrees of freedom, p= 0.82688
SUMMARY of craptest
p-value for no. of wins: 0.631593
p-value for throws/game: 0.826880
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_06:31
No. of wins: Observed Expected
98910 98585.9
z-score= 1.450, pvalue=0.92644
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67322 66666.7 6.442 6.442
2 37573 37654.3 0.176 6.618
3 26714 26954.7 2.150 8.768
4 19446 19313.5 0.910 9.677
5 13715 13851.4 1.344 11.021
6 9885 9943.5 0.345 11.365
7 6913 7145.0 7.535 18.900
8 5147 5139.1 0.012 18.912
9 3698 3699.9 0.001 18.913
10 2706 2666.3 0.591 19.504
11 1871 1923.3 1.424 20.928
12 1376 1388.7 0.117 21.045
13 1011 1003.7 0.053 21.098
14 729 726.1 0.011 21.109
15 517 525.8 0.148 21.258
16 376 381.2 0.070 21.327
17 253 276.5 2.004 23.331
18 212 200.8 0.621 23.952
19 129 146.0 1.976 25.928
20 112 106.2 0.315 26.243
21 295 287.1 0.217 26.460
Chisq= 26.46 for 20 degrees of freedom, p= 0.84885
SUMMARY of craptest
p-value for no. of wins: 0.926436
p-value for throws/game: 0.848847
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0009,0.0076,0.0155,0.0174,0.0180,0.0243,0.0248,0.0255,0.0428,0.0509,
0.0510,0.0545,0.0566,0.0566,0.0603,0.0612,0.0636,0.0639,0.0727,0.0791,
0.0832,0.0886,0.0897,0.0992,0.0998,0.1081,0.1082,0.1096,0.1189,0.1194,
0.1203,0.1244,0.1254,0.1289,0.1329,0.1468,0.1506,0.1550,0.1576,0.1587,
0.1592,0.1623,0.1918,0.1931,0.1943,0.1960,0.1962,0.1981,0.1981,0.1989,
0.1999,0.2033,0.2130,0.2379,0.2391,0.2569,0.2569,0.2643,0.2693,0.2694,
0.2728,0.2783,0.2786,0.2807,0.2807,0.2868,0.2874,0.2901,0.2913,0.2918,
0.2937,0.2976,0.2987,0.3083,0.3121,0.3203,0.3274,0.3359,0.3464,0.3479,
0.3518,0.3560,0.3580,0.3597,0.3602,0.3605,0.3680,0.3724,0.3725,0.3746,
0.3769,0.3772,0.3810,0.3811,0.3858,0.3921,0.3963,0.3979,0.4030,0.4065,
0.4077,0.4085,0.4091,0.4123,0.4296,0.4340,0.4365,0.4380,0.4483,0.4510,
0.4510,0.4539,0.4561,0.4577,0.4578,0.4579,0.4588,0.4600,0.4631,0.4640,
0.4652,0.4774,0.4803,0.4807,0.4812,0.4818,0.4878,0.4901,0.4941,0.4973,
0.4990,0.4995,0.4996,0.5078,0.5097,0.5112,0.5130,0.5193,0.5267,0.5326,
0.5466,0.5560,0.5586,0.5591,0.5623,0.5652,0.5666,0.5702,0.5725,0.5739,
0.5758,0.5764,0.5770,0.5775,0.5790,0.5802,0.5809,0.5812,0.5859,0.5868,
0.5919,0.5933,0.5967,0.6043,0.6086,0.6154,0.6212,0.6236,0.6305,0.6316,
0.6426,0.6459,0.6461,0.6520,0.6554,0.6575,0.6760,0.6771,0.6822,0.6883,
0.6923,0.6957,0.6976,0.6979,0.7123,0.7128,0.7143,0.7335,0.7349,0.7358,
0.7381,0.7387,0.7390,0.7401,0.7431,0.7486,0.7575,0.7620,0.7624,0.7636,
0.7720,0.7767,0.7937,0.7951,0.7994,0.8000,0.8056,0.8074,0.8088,0.8156,
0.8161,0.8171,0.8173,0.8204,0.8218,0.8245,0.8269,0.8296,0.8315,0.8368,
0.8387,0.8431,0.8462,0.8464,0.8472,0.8488,0.8536,0.8603,0.8698,0.8710,
0.8716,0.8720,0.8746,0.8764,0.8764,0.8773,0.8794,0.8860,0.8868,0.8894,
0.8919,0.8932,0.8966,0.9011,0.9033,0.9057,0.9078,0.9086,0.9158,0.9165,
0.9191,0.9264,0.9289,0.9345,0.9383,0.9395,0.9450,0.9618,0.9632,0.9677,
0.9716,0.9728,0.9729,0.9749,0.9867,0.9875,0.9909,0.9922,0.9980,
Overall p-value after applying KStest on 269 p-values = 0.424387
In response to requests, we have provided a list of all the p-values
produced by the tests you have chosen for this run. The individual
p-values are supposed to be uniform in [0,1), but they are not necessarily
independent. So even though we have applied a KSTEST to the accumulated
p-values, the result is not necessarily---even if your file contains truly
random bits---uniform in [0,1). But it is probably pretty close, so take
that last p-value with a grain of salt. In particular, there may be some
values so close to 0 or 1 that the tests they came from should be applied
several more times, or new, related tests should be undertaken.